2x+3=2x+7 7x+3=7x+3 4x+22=8x+10 5x+5=5x+4 3x+18=5x+8 3(4x+8)=4(3x+6) What do you notice about equations that are in each of these categories? Use complete sentences to answer the questions that follow.
- Equations in the first category have the same coefficient for the variable on both sides of the equation. This results in no solution or an infinite number of solutions.
- Equations in the second category have the same expression on both sides of the equation. This results in the statement being true for all values of the variable.
- Equations in the third category have different coefficients and constants on each side of the equation. This results in a single solution for the variable.
- Equations in the fourth category have different constants on each side of the equation, but the same coefficient for the variable. This results in no solution.
- Equations in the fifth category have different coefficients and constants on each side of the equation. This results in a single solution for the variable.
- Equations in the sixth category have different coefficients and constants on each side of the equation, but both sides are equivalent expressions. This results in a single solution for the variable.